On boundary analysis for derivative of driving point impedance functions and its circuit applications

Abstract

In this study, a boundary analysis is carried out for the derivative of driving point impedance (DPI) functions, which is mainly used for the synthesis of networks containing resistor-inductor, resistor–capacitor and resistor–inductor–capacitor circuits. It is known that DPI function, Z ( s ) , is an analytic function defined on the right half of the s-plane. In this study, the authors present four theorems using the modulus of the derivative of DPI function, | Z ′ ( 0 ) | , by assuming the Z ( s ) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of the inequalities obtained in the presented theorems are proved. It is also shown that simple inductor–capacitor tank circuits and higher-order filters are synthesised using the unique DPI functions obtained in each theorem.